An airfoil, such as a propeller blade or a turbine vane or blade (collectively referred to herein as an “airfoil”), may be used in a variety of environments, including different ambient temperatures, gas densities, gas compositions, gas flow rates, pressures and motor rpm. An airfoil shape that is optimized for one environment may have sharply limited application in another environment. For example, vortex shedding at a trailing edge of a rotating airfoil may be tolerable for the nominal design but may become unacceptably high, resulting in airfoil cracking when the manufactured airfoil differs slightly from the specifications. The airfoil design may be constrained by certain physical and/or geometrical considerations that limit the range of airfoil parameters that can be incorporated in the design.
Present designs sometimes lead to extensive airfoil cracking or other failure modes after operation over modest time intervals of the order of a few hours. For example, the vane trailing edge fillet radii for the Space Shuttle Main Engine L.P.O.T.P. (low pressure oxidizer turbopump) have occasionally been observed to develop cracks having a mean crack length of about 0.15 inches. This cracking behavior may arise from strong vortex shedding at the vane trailing edges, compounded by the relatively thin vane trailing edges and/or from the presence of small imperfections in the airfoil trailing edge shape formed in the airfoil manufacturing process.
What is needed is a method for determination of an optimal airfoil shape that provides an approximately optimal shape for a class of environments. This airfoil must be robust enough to operate satisfactorily in these environments and with any reasonable differences from manufacturing specs, and satisfies the constraints imposed on the design. Preferably, the method should be flexible and should be extendible to a larger class of requirements and to changes in the constraints imposed.